Clear evidence for symplectic symmetry in low-lying states of 12C and 16O is reported. Eigenstates of 12C and 16O, determined within the framework of the no-core shell model using the J-matrix inverse scattering potential with A
The quantum deformation concept is applied to a study of pairing correlations in nuclei with mass 40< or =A< or =100. While the nondeformed limit of the theory provides a reasonable overall description of certain nuclear properties and fine structure effects, the results show that the q deformation plays a significant role in understanding higher-order effects in the many-body interaction.
The no-core shell model (NCSM) is a prominent ab initio method that yields a good description of the low-lying states in few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless, its applicability is limited by the rapid growth of the many-body basis with larger model spaces and increasing number of nucleons. The symplectic no-core shell model (Sp-NCSM) aspires to extend the scope of the NCSM beyond the p-shell region by augmenting the conventional spherical harmonic oscillator basis with the physically relevant symplectic Sp(3, R) symmetry-adapted configurations of the symplectic shell model that describe naturally the monopole-quadrupole vibrational and rotational modes, and also partially incorporate α-cluster correlations. In this review, the models underpinning the Sp-NCSM approach, namely, the NCSM, the Elliott SU(3) model and the symplectic shell model, are discussed. Following this, a prescription for constructing translationally invariant symplectic configurations in the spherical harmonic oscillator basis is given. This prescription is utilized to unveil the extent to which symplectic configurations enter into low-lying states in 12 C and 16 O nuclei calculated within the framework of the NCSM with the JISP16 realistic nucleon-nucleon interaction. The outcomes of this proof-of-principle study are presented in detail.
The symplectic Sp(3, R) symmetry of eigenstates for the 16 O ground state and the 0 + gs and lowest 2 + and 4 + configurations of 12 C that are determined within the framework of the no-core shell model with the JISP16 realistic interaction is examined. These states are found to project at the 80-85% level onto a few 0-particle-0-hole symplectic representations, including the most deformed configuration. The corresponding symplectic space spans 0-particle-0-hole nuclear configurations together with single-and multiparticle excitations. The results are nearly independent of the harmonic oscillator strength and whether the bare or renormalized effective interactions are used in the analysis. The outcome points to the relevance of a symplectic no-core shell model and reaffirms the Elliott SU(3) model on which the symplectic scheme is built.
A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0 + ground states, they also have a large effect on the energies of excited states, including especially excited 0 + states. In this article we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp (q) (4) to different realizations of u (q) (2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0 + states of even-even and odd-odd nuclei in the 1d 3/2 , 1f 7/2 , and 1f 5/2 2p 1/2 2p 3/2 1g 9/2 shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Sp q (4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton-neutron interaction along with non-linear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0 + energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking, and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher-order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.
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